Intermediate Algebra (6th Edition)

by
Martin-Gay, Elayn

Answer

$\dfrac{x-1}{x-2\sqrt{x}+1}$

Work Step by Step

Multiplying by the conjugate of the numerator, then the rationalized-numerator form of the given expression, $
\dfrac{\sqrt{x}+1}{\sqrt{x}-1}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\cdot\dfrac{\sqrt{x}-1}{\sqrt{x}-1}
\\\\=
\dfrac{(\sqrt{x})^2-1^2}{(\sqrt{x}-1)^2}
\\\\=
\dfrac{x-1}{(\sqrt{x})^2+2(\sqrt{x})(-1)+(-1)^2}
\\\\=
\dfrac{x-1}{x-2\sqrt{x}+1}
.\end{array}